Two-loop mass anomalous dimension in reduced quantum electrodynamics and application to dynamical fermion mass generation

We consider reduced quantum electrodynamics (RQED$_{d_\gamma,d_e}$) a model describing fermions in $d_e$-dimensional space-time and interacting via the exchange of massless bosons $d_\gamma$-dimensions ($d_e \leq d_\gamma$). compute two-loop mass anomalous dimension, $\gamma_m$, general RQED$_{4,d_e}$ with applications to RQED$_{4,3}$ QED$_4$. then proceed on studying dynamical (parity-even) fermion generation by constructing fully gauge-invariant gap equation for $\gamma_m$ as only input. This allows straightforward analytic computation critical coupling constant, $\alpha_c$, which is such that generated $\alpha_r > \alpha_c$, where $\alpha_r$ renormalized well number flavours, $N_c$, $\alpha_c \rightarrow \infty$ $N < N_c$. For RQED$_{4,3}$, our results are perfect agreement more elaborate analysis based resolution truncated Schwinger-Dyson equations at order. In case QED$_4$, analytical (that use state art five-loop expression $\gamma_m$) good quantitative those obtained from numerical approaches.